Best Known (126, 126+102, s)-Nets in Base 4
(126, 126+102, 130)-Net over F4 — Constructive and digital
Digital (126, 228, 130)-net over F4, using
- t-expansion [i] based on digital (105, 228, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(126, 126+102, 229)-Net over F4 — Digital
Digital (126, 228, 229)-net over F4, using
(126, 126+102, 3211)-Net in Base 4 — Upper bound on s
There is no (126, 228, 3212)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 188118 549176 803864 582428 162402 443006 476359 574250 147207 345853 299872 632293 142730 404123 458549 357951 868990 491193 990562 118852 236929 816177 586600 > 4228 [i]